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arxiv: 2407.08721 · v2 · pith:ONHW52MDnew · submitted 2024-07-11 · ⚛️ nucl-th · hep-lat· hep-ph· nucl-ex

A unitary coupled-channel three-body amplitude with pions and kaons

Yuchuan Feng , Fernando Gil , Michael D\"oring , Raquel Molina , Maxim Mai , Vanamali Shastry , Adam Szczepaniak This is my paper
classification ⚛️ nucl-th hep-lathep-phnucl-ex
keywords amplitudecoupled-channelthree-bodyamplitudesisobarskaonspionsprinciple
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Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, re-arranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems ("isobars") of all isospins, $I=0,\,1/2,\,1,\, 3/2, \, 2$, and it also allows for transitions within a given isobar. The $f_0(500)\, ("\sigma"),\,f_0(980),\,\rho(700), K_0^*(700)\,("\kappa")$, and $K^*(892)$ resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for $a_1$ quantum numbers are shown as a proof of principle for the numerical implementation.

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